And that’s one of the reasons why a big part of the rest of the world think that the people living in the USA are rude. It’s not just about needless interactions, you don’t interact at all. No hi, no please, no thanks, no goodbye, no have a nice day, no sorry, no time. I’m glad I never learnt how to be rude and that’s not a skill I’ll try to teach my kids.

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I may be wrong or have misunderstood what you said but the sets of natural numbers and odd numbers have the same size/cardinality. If there exists a bijection between the two sets then they have the same size.

f(x) = 2x + 1 is such a bijection

For the same reason, N, Z and Q have the same cardinality. The fact that each one is included in the next ones doesn’t mean their size is different.